Among the various alternatives to renormalisation, one may single out the \(  \texttt {S}  \) -matrix program which aimed at describing a quantum field theory
directly in terms of the quantities that are measured in experiments. This led to a formulation of the theory in terms of matrix valued functions in \(n\)  complex variables, with \(n=0,1,2,\dots \) ,
that correspond to the entries of the \(  \texttt {S}  \) -matrix between asymptotic states.
The \(  \texttt {S}  \) -matrix program was actively investigated in the 60s and 70s and numerous attempts were made to characterise the \(  \texttt {S}  \) -matrix which is the central object in this approach, see e.g. [1]}, [2]}. However, these investigations led to rather
unsatisfactory results in spacial dimensions higher than one, mainly due to the incapacity of constructing viable, explicit, \(  \texttt {S}  \) -matrices
for non-trivial models.
